On selection rules in two-dimensional terahertz-infrared-visible spectroscopy.

Two-dimensional terahertz-infrared-visible (2D TIRV) spectroscopy directly measures the coupling between quantum high-frequency vibrations and classical low-frequency modes of molecular motion. In addition to coupling strength, the signal intensity in 2D TIRV spectroscopy can also depend on the selection rules of the excited transitions. Here, we explore the selection rules in 2D TIRV spectroscopy by studying the coupling between the high-frequency CH3 stretching and low-frequency vibrations of liquid dimethyl sulfoxide (DMSO). Different excitation pathways are addressed using variations in laser pulse timing and different polarizations of exciting pulses and detected signals. The DMSO signals generated via different excitation pathways can be readily distinguished in the spectrum. The intensities of different excitation pathways vary unequally with changes in polarization. We explain how this difference stems from the intensities of polarized and depolarized Raman and hyper-Raman spectra of high-frequency modes. These results apply to various systems and will help design and interpret new 2D TIRV spectroscopy experiments.

Experimental Access to Mode-Specific Coupling between Quantum Molecular Vibrations and Classical Bath Modes.

The interaction of quantum-mechanical systems with a fluctuating thermal environment (bath) is fundamental to molecular mechanics and energy transport/dissipation. Its complete picture requires mode-specific measurements of this interaction and an understanding of its nature. Here, we present a combined experimental and theoretical study providing detailed insights into the coupling between a high-frequency vibrational two-level system and thermally excited terahertz modes. Experimentally, two-dimensional terahertz-infrared-visible spectroscopy reports directly on the coupling between quantum oscillators represented by CH3 streching vibrations in liquid dimethyl sulfoxide and distinct low-frequency modes. Theoretically, we present a mixed quantum-classical formalism of the sample response to enable the simultaneous quantum description of high-frequency oscillators and a classical description of the bath. We derive the strength and nature of interaction and find different coupling between CH3 stretch and low-frequency modes. This general approach enables quantitative and mode-specific analysis of coupled quantum and classical dynamics in complex chemical systems.

Controlling the electro-optic response of a semiconducting perovskite coupled to a phonon-resonant cavity.

Optical cavities, resonant with vibrational or electronic transitions of material within the cavity, enable control of light-matter interaction. Previous studies have reported cavity-induced modifications of chemical reactivity, fluorescence, phase behavior, and charge transport. Here, we explore the effect of resonant cavity-phonon coupling on the transient photoconductivity in a hybrid organic-inorganic perovskite. To this end, we measure the ultrafast photoconductivity response of perovskite in a tunable Fabry-Pérot terahertz cavity, designed to be transparent for optical excitation. The terahertz-cavity field-phonon interaction causes apparent Rabi splitting between the perovskite phonon mode and the cavity mode. We explore whether the cavity-phonon interaction affects the material's electron-phonon interaction by determining the charge-carrier mobility through photoconductivity. Despite the apparent hybridization of cavity and phonon modes, we show that the perovskite properties in both ground (phonon response) and excited (photoconductive response) states remain unaffected by the tunable light-matter interaction. Yet the response of the integral perovskite-terahertz optical cavity system depends critically on the interaction strength of the cavity with the phonon: the transient terahertz response to optical excitation can be increased up to threefold by tuning the cavity-perovskite interaction strength. These results enable tunable switches and frequency-controlled induced transparency devices.

Extracting the sample response function from experimental two-dimensional terahertz-infrared-visible spectra.

Terahertz molecular motions are often probed by high-frequency molecular oscillators in different types of non-linear vibrational spectroscopy. Recently developed two-dimensional terahertz-infrared-visible spectroscopy allows direct measuring of this coupling and, thus, obtaining site-specific terahertz vibrational spectrum. However, these data are affected by the intensity and phase of the employed laser pulses. In this work, we develop a method of extracting sample response-representing solely physical properties of a material-from experimental spectra. Using dimethyl sulfoxide as a model molecule to verify this method, we measure the coupling between C-H stretch vibration of its methyl groups and terahertz intramolecular twist and wagging modes.

Passively Stabilized Phase-Resolved Collinear SFG Spectroscopy Using a Displaced Sagnac Interferometer.

Sum-frequency generation (SFG) vibrational spectroscopy is a powerful technique to study interfaces at the molecular level. Phase-resolved SFG (PR-SFG) spectroscopy provides direct information on interfacial molecules' orientation. However, its implementation is technologically demanding: it requires the generation of a local oscillator wave and control of its time delay with sub-fs accuracy. Commonly used noncollinear PR-SFG provides this control naturally but requires very accurate sample height control. Collinear PR-SFG spectroscopy is less demanding regarding sample positioning, but tuning the local oscillator time delay with this beam geometry is challenging. Here, we develop a collinear PR-SFG setup using a displaced Sagnac interferometer. This scheme allows full, independent control of the time delay and intensity of the local oscillator and provides long-time phase stabilization (better than 5° over 12 h) for the measured signal. This approach substantially reduces the complexity of an experimental setup and combines the advantages of collinear and noncollinear PR-SFG techniques.

Distinguishing different excitation pathways in two-dimensional terahertz-infrared-visible spectroscopy.

In condensed molecular matter, low-frequency modes (LFMs) associated with specific molecular motions are excited at room temperature and determine essential physical and chemical properties of materials. LFMs, with typical mode energies of up to ∼500 cm-1 (62 meV), contribute significantly to thermodynamic parameters and functions (e.g., heat capacity and entropy) and constitute the basis for room temperature molecular dynamics (e.g., conformational fluctuations and change). LFMs are often analyzed indirectly by the measurement of their effect on specific high-frequency modes (HFMs); the LFM-HFM coupling is reflected in the lineshape, as well as in the spectral and angular diffusion of the HFM. Two-dimensional terahertz-infrared-visible (2D TIRV) spectroscopy allows measuring the LFM-HFM coupling directly and can thereby provide new insights into the strength and nature of the coupling and the character of LFMs. However, the interference between the different signals generated by different excitation pathways can complicate 2D TIRV spectra, preventing a straightforward analysis. Here, we develop an experimental method to distinguish different excitation pathways in 2D TIRV spectroscopy and plot them separately in different quadrants of a 2D spectrum. We validate this method by measuring the spectra of CaF2 and nitrogen gas. For CaF2, only sum-frequency mixing between infrared and terahertz fields generates the signal. In contrast, for N2, only difference-frequency mixing is observed. We then use this method to separate sum- and difference-frequency pathways in the 2D TIRV spectrum of liquid water, verifying the previous interpretation of the lineshape of the 2D TIRV spectrum of water.

Composition-Dependent Hydrogen-Bonding Motifs and Dynamics in Brønsted Acid-Base Mixtures.

In recent years the interaction of organophosphates and imines, which is at the core of Brønsted acid organocatalysis, has been established to be based on strong ionic hydrogen bonds. Yet, besides the formation of homodimers consisting of two acid molecules and heterodimers consisting of one acid and one base, also multimeric molecular aggregates are formed in solution. These multimeric aggregates consist of one base and several acid molecules. The details of the intermolecular bonding in such aggregates, however, have remained elusive. To characterize composition-dependent bonding and bonding dynamics in these aggregates, we use linear and nonlinear infrared (IR) spectroscopy at varying molar ratios of diphenyl phosphoric acid and quinaldine. We identify the individual aggregate species, giving rise to the structured, strong, and very broad infrared absorptions, which span more than 1000 cm-1. Linear infrared spectra and density functional theory calculations of the proton transfer potential show that doubly ionic intermolecular hydrogen bonds between the acid and the base lead to absorptions which peak at ∼2040 cm-1. The contribution of singly ionic hydrogen bonds between an acid anion and an acid molecule is observed at higher frequencies. As common to such strong hydrogen bonds, ultrafast IR spectroscopy reveals rapid, ∼ 100 fs, dissipation of energy from the proton transfer coordinate. Yet, the full dissipation of the excess energy occurs on a ∼0.8-1.1 ps time scale, which becomes longer when multimers dominate. Our results thus demonstrate the coupling and collectivity of the hydrogen bonds within these complexes, which enable efficient energy transfer.

Dynamics of Dicyanamide in Ionic Liquids is Dominated by Local Interactions.

The dynamics of probe molecules is commonly used to investigate the structural dynamics of room-temperature ionic liquids; however, the extent to which this dynamics reflects the dynamics of the ionic liquids or is probe specific has remained debated. Here, we explore to what extent the vibrational and rotational dynamics of the dicyanamide anion, a common ionic liquid anion, correlates with the structural relaxation of ionic liquids. We use polarization-resolved, ultrafast infrared spectroscopy to probe the temperature- and probe-concentration-dependent dynamics of samples with small amounts of 1-ethyl-3-methylimidazolium ([emim]+) dicyanamide ([DCA]-) dissolved in four [emim]+-based ionic liquids with tetrafluoroborate ([BF4]-), bis(trifluoromethylsulfonyl)imide ([NTf2]-), ethylsufate ([EtSO4]-), and triflate ([OTf]-) as anions. The transient spectra after broad-band excitation at 2000-2300 cm-1, resonant with the symmetric and antisymmetric C≡N stretching vibrations, initially contain oscillatory signatures due to the vibrational coherence between both modes. Vibrational population relaxation occurs on two distinct time scales, ∼6-7 and ∼15-20 ps. The vibrational dynamics is rather insensitive to the details of the ionic liquid anion and temperature, except for the slow vibrational relaxation component. The decay of the excitation anisotropy, a measure of the rotational dynamics of [DCA]-, markedly depends on temperature, and the obtained decay time exhibits an activation energy of ∼15-21 kJ/mol. Remarkably, neither the rotation time nor the activation energy can be simply explained by the variation of the macroscopic viscosity. Hence, our results suggest that the dynamics of dicyanamide is only in part representative of the ionic liquid structural dynamics. Rather, the dynamics of the probe anion seems to be determined by the specific interaction of [DCA]- with the ionic liquid's ions for the class of [emim]+-based ionic liquids studied here.

Vibrational Coupling between Organic and Inorganic Sublattices of Hybrid Perovskites.

The interplay of electronic and nuclear degrees of freedom in semiconductor hybrid organic-inorganic perovskites determines many of their fundamental photophysical properties. For instance, charge carriers are dressed with phonons, that is, form polarons, and combination modes composed of strongly mixed localized vibrations and delocalized phonons can provide pathways for electronic energy relaxation and dissipation. Mixing of the different types of nuclear motion in vibrational combination modes requires their strong coupling. The direct measurement of coupling between the high-frequency N-H stretch modes of the organic methylammonium and formamidinium ions and low-frequency Pb-I phonon modes of the inorganic sub-lattice in hybrid organic-inorganic perovskites is presented. The results reveal direct and substantial coupling between the non-covalently interacting organic and inorganic sub-lattices.

Coupling between intra- and intermolecular motions in liquid water revealed by two-dimensional terahertz-infrared-visible spectroscopy.

The interaction between intramolecular and intermolecular degrees of freedom in liquid water underlies fundamental chemical and physical phenomena such as energy dissipation and proton transfer. Yet, it has been challenging to elucidate the coupling between these different types of modes. Here, we report on the direct observation and quantification of the coupling between intermolecular and intramolecular coordinates using two-dimensional, ultra-broadband, terahertz-infrared-visible (2D TIRV) spectroscopy and molecular dynamics calculations. Our study reveals strong coupling of the O-H stretch vibration, independent of the degree of delocalization of this high-frequency mode, to low-frequency intermolecular motions over a wide frequency range from 50 to 250 cm-1, corresponding to both the intermolecular hydrogen bond bending (≈ 60 cm-1) and stretching (≈ 180 cm-1) modes. Our results provide mechanistic insights into the coupling of the O-H stretch vibration to collective, delocalized intermolecular modes.

Time-Resolved Sum Frequency Generation Spectroscopy: A Quantitative Comparison Between Intensity and Phase-Resolved Spectroscopy.

Time-resolved and two-dimensional sum frequency generation (TR-SFG and 2D-SFG) spectroscopies are promising tools in the experimental study of molecular dynamics, specifically at interfaces. Most implementations of TR/2D-SFG spectroscopy rely on a pump-probe scheme, where an excitation pulse excites a fraction of interfacial molecules into the first excited state of a specific vibrational mode, and a subsequent SFG probe pair detects the time-dependent changes of the surface vibrational response. In steady state SFG spectroscopy, phase-resolved detection (also known as heterodyne-detection), as opposed to SFG intensity measurements, has been shown to be useful in unraveling the steady-state response of interfacial vibrations. Here, we explore the merits of phase-resolved TR/2D-SFG spectroscopy. This purely theoretical and numerical study reveals that, for a typical response from aqueous interfaces, the intensity 2D-SFG measurements contain the same information content as phase-resolved 2D-SFG measurements. We specifically analyze the frequency-dependence of the bleach lifetime (reflecting vibrational relaxation), and the time-dependent slope of the on-diagonal features observed in a 2D spectra. We show that for different systems, the intensity-based and phase-resolved 2D-SFG measurements provide the same information and are quantitatively very similar. We investigate the effect of different lineshapes, anharmonicity, and nonresonant signal contributions, and show that none of these effects substantially change the conclusion that intensity-based and phase-resolved 2D-SFG measurements provide equivalent information.

Direct observation of mode-specific phonon-band gap coupling in methylammonium lead halide perovskites.

Methylammonium lead iodide perovskite is an outstanding semiconductor for photovoltaics. One of its intriguing peculiarities is that the band gap of this perovskite increases with increasing lattice temperature. Despite the presence of various thermally accessible phonon modes in this soft material, the understanding of how precisely these phonons affect macroscopic material properties and lead to the peculiar temperature dependence of the band gap has remained elusive. Here, we report a strong coupling of a single phonon mode at the frequency of ~ 1 THz to the optical band gap by monitoring the transient band edge absorption after ultrafast resonant THz phonon excitation. Excitation of the 1 THz phonon causes a blue shift of the band gap over the temperature range of 185 ~ 300 K. Our results uncover the mode-specific coupling between one phonon and the optical properties, which contributes to the temperature dependence of the gap in the tetragonal phase.Methylammonium lead iodide perovskite, a promising material for efficient photovoltaics, shows a unique temperature dependence of its optical properties. Kim et al. quantify the coupling between the optical gap and a lattice phonon at 1 THz, which favorably contributes to the thermal variation of the gap.

Isotope-Labeled Amyloids via Synthesis, Expression, and Chemical Ligation for Use in FTIR, 2D IR, and NMR Studies.

This chapter provides protocols for isotope-labeling the human islet amyloid polypeptide (hIAPP or amylin) involved in type II diabetes and γD-crystallin involved in cataract formation. Because isotope labeling improves the structural resolution, these protocols are useful for experiments using Fourier transform infrared (FTIR), two-dimensional infrared (2D IR), and NMR spectroscopies. Our research group specializes in using 2D IR spectroscopy and isotope labeling. 2D IR spectroscopy provides structural information by measuring solvation from 2D diagonal lineshapes and vibrational couplings from cross peaks. Infrared spectroscopy can be used to study kinetics, membrane proteins, and aggregated proteins. Isotope labeling provides greater certainty in the spectral assignment, which enables new structural insights that are difficult to obtain with other methods. For amylin, we provide a protocol for (13)C/(18)O labeling backbone carbonyls at one or more desired amino acids in order to obtain residue-specific structural resolution. We also provide a protocol for expressing and purifying amylin from E. coli, which enables uniform (13)C or (13)C/(15)N labeling. Uniform labeling is useful for measuring the monomer infrared spectrum in an amyloid oligomer or fiber as well as amyloid protein bound to another polypeptide or protein, such as a chaperone or an inhibitor. In addition, our expression protocol results in 2-2.5 mg of amylin peptide per 1 L cell culture, which is a high enough yield to straightforwardly obtain the 2-10 mg needed for high resolution and solid-state NMR experiments. Finally, we provide a protocol to isotope-label either of the two domains of γD-crystallin using expressed protein ligation. Domain labeling makes it possible to resolve the structures of the two halves of the protein in FTIR and 2D IR spectra. With modifications, these strategies and protocols for isotope labeling can be applied to other amyloid polypeptides and proteins.

Transition Dipoles from 1D and 2D Infrared Spectroscopy Help Reveal the Secondary Structures of Proteins: Application to Amyloids.

Transition dipoles are an underutilized quantity for probing molecular structures. The transition dipole strengths in an extended system like a protein are modulated by the couplings and thus probe the structures. Here we measure the absolute transition dipole strengths of human and rat amylin in their solution, aggregated, membrane, and micelleular bound forms, using a combination of 1D and 2D infrared spectroscopy. We find that the vibrational modes of amyloid fibers made of human amylin can extend across as many as 12 amino acids, reflecting very ordered ß-sheets in the most carefully prepared samples. Rat amylin has FTIR spectra that are nearly identical in solution, micelles, and membranes. We show that the transition dipoles of rat amylin are much larger when bound to micelles and membranes than when in solution, consistent with rat amylin adopting an α-helical structure. We interpret the transition dipole strengths as experimental measurements of the inverse participation ratio often calculated in theoretical studies. The structure of aggregating and membrane-bound proteins can be difficult to identify with existing techniques, especially during kinetics. These results demonstrate how absolute transition dipoles measured via our 1D/2D spectroscopy method can provide important structural information.

Background-Free Fourth-Order Sum Frequency Generation Spectroscopy.

The recently developed 2D sum frequency generation spectroscopy offers new possibilities to analyze the structure and structural dynamics of interfaces in a surface-specific manner. Its implementation, however, has so far remained limited to the pump-probe geometry, with its inherent restrictions. Here we present 2D SFG experiments utilizing a novel noncollinear geometry of four incident laser pulses generating a 2D SFG response, analogous to the triangle geometry applied in bulk-sensitive 2D infrared spectroscopy. This approach allows for background-free measurements of fourth-order nonlinear signals, which is demonstrated by measuring the fourth-order material response from a GaAs (110) surface. The implementation of phase-sensitive detection and broadband excitation pulses allows for both highest possible time resolution and high spectral resolution of the pump axis of a measured 2D SFG spectrum. To reduce the noise in our spectra, we employ a referencing procedure, for which we use noncollinear pathways and individual focusing for the signal and local oscillator beams. The 2D spectra recorded from the GaAs (110) surface show nonzero responses for the real and imaginary component, pointing to contributions from resonant electronic pathways to the χ((4)) response.

Energy transfer pathways in semiconducting carbon nanotubes revealed using two-dimensional white-light spectroscopy.

Thin film networks of highly purified semiconducting carbon nanotubes (CNTs) are being explored for energy harvesting and optoelectronic devices because of their exceptional transport and optical properties. The nanotubes in these films are in close contact, which permits energy to flow through the films, although the pathways and mechanisms for energy transfer are largely unknown. Here we use a broadband continuum to collect femtosecond two-dimensional white-light spectra. The continuum spans 500 to 1,300 nm, resolving energy transfer between all combinations of bandgap (S1) and higher (S2) transitions. We observe ultrafast energy redistribution on the S2 states, non-Förster energy transfer on the S1 states and anti-correlated energy levels. The two-dimensional spectra reveal competing pathways for energy transfer, with S2 excitons taking routes depending on the bandgap separation, whereas S1 excitons relax independent of the bandgap. These observations provide a basis for understanding and ultimately controlling the photophysics of energy flow in CNT-based devices.

Diffusion-assisted photoexcitation transfer in coupled semiconducting carbon nanotube thin films.

We utilize femtosecond transient absorption spectroscopy to study dynamics of photoexcitation migration in films of semiconducting single-wall carbon nanotubes. Films of nanotubes in close contact enable energy migration such as needed in photovoltaic and electroluminescent devices. Two types of films composed of nanotube fibers are utilized in this study: densely packed and very porous. By comparing exciton kinetics in these films, we characterize excitation transfer between carbon nanotubes inside fibers versus between fibers. We find that intrafiber transfer takes place in both types of films, whereas interfiber transfer is greatly suppressed in the porous one. Using films with different nanotube composition, we are able to test several models of exciton transfer. The data are inconsistent with models that rely on through-space interfiber energy transfer. A model that fits the experimental results postulates that interfiber transfer occurs only at intersections between fibers, and the excitons reach the intersections by diffusing along the long-axis of the tubes. We find that time constants for the inter- and intrafiber transfers are 0.2-0.4 and 7 ps, respectively. In total, hopping between fibers accounts for about 60% of all exciton downhill transfer prior to 4 ps in the dense film. The results are discussed with regards to transmission electron micrographs of the films. This study provides a rigorous analysis of the photophysics in this new class of promising materials for photovoltaics and other technologies.

Photoexcitation dynamics of coupled semiconducting carbon nanotube thin films.

Carbon nanotubes are a promising means of capturing photons for use in solar cell devices. We time-resolved the photoexcitation dynamics of coupled, bandgap-selected, semiconducting carbon nanotubes in thin films tailored for photovoltaics. Using transient absorption spectroscopy and anisotropy measurements, we found that the photoexcitation evolves by two mechanisms with a fast and long-range component followed by a slow and short-range component. Within 300 fs of optical excitation, 20% of nanotubes transfer their photoexcitation over 5-10 nm into nearby nanotube fibers. After 3 ps, 70% of the photoexcitation resides on the smallest bandgap nanotubes. After this ultrafast process, the photoexcitation continues to transfer on a ~10 ps time scale but to predominantly aligned tubes. Ultimately the photoexcitation hops twice on average between fibers. These results are important for understanding the flow of energy and charge in coupled nanotube materials and light-harvesting devices.

Quantification of transition dipole strengths using 1D and 2D spectroscopy for the identification of molecular structures via exciton delocalization: application to α-helices.

Vibrational and electronic transition dipole strengths are often good probes of molecular structures, especially in excitonically coupled systems of chromophores. One cannot determine transition dipole strengths using linear spectroscopy unless the concentration is known, which in many cases it is not. In this paper, we report a simple method for measuring transition dipole moments from linear absorption and 2D IR spectra that does not require knowledge of concentrations. Our method is tested on several model compounds and applied to the amide I(') band of a polypeptide in its random coil and α-helical conformation as modulated by the solution temperature. It is often difficult to confidently assign polypeptide and protein secondary structures to random coil or α-helix by linear spectroscopy alone, because they absorb in the same frequency range. We find that the transition dipole strength of the random coil state is 0.12 ± 0.013 D(2), which is similar to a single peptide unit, indicating that the vibrational mode of random coil is localized on a single peptide unit. In an α-helix, the lower bound of transition dipole strength is 0.26 ± 0.03 D(2). When taking into account the angle of the amide I(') transition dipole vector with respect to the helix axis, our measurements indicate that the amide I(') vibrational mode is delocalized across a minimum of 3.5 residues in an α-helix. Thus, one can confidently assign secondary structure based on exciton delocalization through its effect on the transition dipole strength. Our method will be especially useful for kinetically evolving systems, systems with overlapping molecular conformations, and other situations in which concentrations are difficult to determine.